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Block #2,094,787

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2017, 8:36:47 PM Β· Difficulty 10.8720 Β· 4,748,386 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
1dadaa6beae67460e687a68403a6451c0211c1ce0481302265581f3cdc42b9d8
View on Chainz β†—

Height

#2,094,787

Difficulty

10.872007

Transactions

1

Size

199 B

Version

2

Bits

0adf3bde

Nonce

519,202,240

Timestamp

4/30/2017, 8:36:47 PM

Confirmations

4,748,386

Mined by

⛏️ P2SHARQq4uaUsWf7J4spsxZrnpXFUGq4xRDHfi

Merkle Root

87c30f49e11e6768c6b5b97508f2d01e288449ceb777bfa9883b482f0e99e578
Transactions (1)
Coinbase87c30f49e11e67…3b482f0e99e578
1 in β†’ 1 out8.4500 XPM109 B
ARQq4uaU…q4xRDHfi
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.095 Γ— 10⁹⁴(95-digit number)
70959900168815244002…17874530176447083841
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
7.095 Γ— 10⁹⁴(95-digit number)
70959900168815244002…17874530176447083841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.419 Γ— 10⁹⁡(96-digit number)
14191980033763048800…35749060352894167681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.838 Γ— 10⁹⁡(96-digit number)
28383960067526097600…71498120705788335361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.676 Γ— 10⁹⁡(96-digit number)
56767920135052195201…42996241411576670721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.135 Γ— 10⁹⁢(97-digit number)
11353584027010439040…85992482823153341441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.270 Γ— 10⁹⁢(97-digit number)
22707168054020878080…71984965646306682881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.541 Γ— 10⁹⁢(97-digit number)
45414336108041756161…43969931292613365761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.082 Γ— 10⁹⁢(97-digit number)
90828672216083512322…87939862585226731521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.816 Γ— 10⁹⁷(98-digit number)
18165734443216702464…75879725170453463041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.633 Γ— 10⁹⁷(98-digit number)
36331468886433404929…51759450340906926081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,989,750 XPMΒ·at block #6,843,172 Β· updates every 60s
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